Laying eye shapes on a curved character head surface
1 Select your cylinder.
2 In properties select the chain link icon.
3 Select in [Add Object Constraint] the "Track to" option.
4 Target: choose the sphere. NOTE: The origin of both objects should be in their center for this to work. 
5 Try different "To:" and "Up:" combinations until the flat side of the cylinder is aiming at the sphere.
6 To move the cylinder against the sphere use the translation manipulator, it normally says: "Global" next to it, change that to "Normal" and one of the manipulators arrows will align to the sphere to allow you to translate it till they connect.